Distance Time problem

[Vemuri]

Timothy leaves home for school, riding his bicycle at a rate of 9mph. 15mins after he leaves, his mother sees Timothy's math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36mph, how far (in terms of miles) must she drive before she reaches Timothy?

A. 1/3
B. 3
C. 4
D. 9
E. 12

[cramya]

These dist/rate/time problems can be solved if u use a grid meaning generic template.

See attached. Hope this helps!

Regards,
CR

[daimaomee]

Assume Tim's mother catches up with Tim after riding for t hours, at that time, Tim's mother is 36t miles from home and Tim is 9(t + 1/4) miles from home

Therefore 36t = 9(t + 1/4)

Solving for t, we get t = 1/12 and therefore distance that Tim's mother has driven by 36/12 = 3 miles

Therefore, answer should be B

[sureshbala]

Her mother gains 3 hrs over a distance of 36 miles. (I mean to say to travel 36 miles Timothy takes 4 hrs while her mother takes 1 hr) In order to reach Timothy she must gain 1/4 hr for which she has to travel 1/12(36) = 3 miles.

[anniev2]

This question makes absolutely no sense to me. Can someone else please explain how this answer is given.

[welcome]

Timothy will travel 15 minuts and the the same time what her mother will take to reach her.

so 15/60*9 + 9T = 36 T => T = 3/36

So distance travel by Mom = 36 * 3/36 = 3. Ans.

[anniev2]

Thanks! That helped me to understand the concept better. Here is how I found the correct answer. Its elementary but its good for those (like me) that may not of known how to start solving the problem:

Determine how many miles Tim is away from the house when his mother leaves home at the 15 minute mark:

d=rt
d= 9 mph * 1/4
d= 9 / 4 = 2.25 miles, distance Timothy has traveled from home in 15 minutes
(Note: this is at a rate of 3/4 or 0.75 miles per every 5 minutes)

Determine how many miles Mom is from home 5 minutes after she leaves (Timothy has been traveling for 20 minutes at this point)

d=rt
d= 36 mph * 1/12
d = 36 / 12 = 3 miles, distance Mom has traveled from home in 5 minutes

If Timothy travels at a rate of 0.75 or 3/4 miles every 5 minutes and he traveled 2.25 miles in 15 minutes then in 20 minutes he travels 3 miles. Since mom left home 15 minutes after Timothy and travels at a rate of 3 miles every 5 minutes then when Timothy has travelled 20 minutes and she has traveled 5 minutes they have both traveled 3 miles and they meet up.